Moles Calculators

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The mole (mol) is the SI base unit for the amount of substance, defined as exactly 6.02214076 × 10²³ elementary entities (atoms, molecules, ions, or other particles) — Avogadro's number (Nₐ). One mole of any substance contains the same number of entities. The molar mass (in g/mol) equals the mass of one mole of a substance and numerically equals the atomic or molecular weight from the periodic table. Moles bridge the macroscopic world (grams, liters) and the molecular world (atoms, molecules), enabling stoichiometric calculations that lie at the heart of chemistry.

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Key Mole Relationships

n (mol) = mass (g) / molar mass (g/mol)

n (mol) = molecules / Avogadro's number (6.022 × 10²³)

n (mol) = M (mol/L) × V (L) [for solutions]

Molar mass = atomic/molecular weight (from periodic table) in g/mol

Worked Examples

How many moles in 25.0 g of NaCl (MW = 58.44 g/mol)?
n = 25.0/58.44 = 0.428 mol.

How many molecules in 0.428 mol NaCl?
molecules = 0.428 × 6.022 × 10²³ = 2.58 × 10²³ molecules.

How many moles of glucose (MW = 180.16) in 500 mL of 0.25 M solution?
n = 0.25 × 0.500 = 0.125 mol. Mass = 0.125 × 180.16 = 22.5 g.

Avogadro's Number

Nₐ = 6.02214076 × 10²³ mol⁻¹. The mole is defined so that 12 g of carbon-12 contains exactly Nₐ atoms. At standard temperature and pressure (STP: 0°C, 1 bar), 1 mol of ideal gas occupies 22.4 L (molar volume). This relationship is used in gas stoichiometry calculations.

Using Moles in Stoichiometry

Balanced equations give molar ratios: N₂ + 3H₂ → 2NH₃. From 7.0 g N₂ (MW = 28.0): n = 7.0/28 = 0.25 mol N₂; requires 0.75 mol H₂ (ratio 1:3); produces 0.50 mol NH₃. Mass NH₃ = 0.50 × 17.0 = 8.5 g.

Glossary

Mole (mol)
The SI unit for amount of substance: 1 mol = 6.02214076 × 10²³ entities (Avogadro's number); n = mass/molar mass; bridges macroscopic masses to molecular counts.
Avogadro's Number (Nₐ)
6.02214076 × 10²³ mol⁻¹; the number of entities in one mole; defined so that 12 g of carbon-12 contains exactly Nₐ atoms.
Molar Mass
The mass of one mole of a substance in g/mol; numerically equals the molecular weight in amu/Daltons; used to convert between grams and moles.

Frequently Asked Questions

A mole (mol) is the SI unit for amount of substance, containing exactly 6.02214076 × 10²³ entities (atoms, molecules, ions, electrons, etc.) — Avogadro's number. One mole of any substance contains the same number of particles, but different masses (1 mol C = 12 g; 1 mol H₂O = 18 g; 1 mol NaCl = 58.5 g). The mole bridges the macroscopic (grams) and molecular (atoms) worlds: n (mol) = mass (g) / molar mass (g/mol). It allows chemists to work with countable quantities of atoms without dealing with individual tiny masses.

n (mol) = mass (g) / molar mass (g/mol). To find molar mass: sum the atomic masses of all atoms in the formula (from the periodic table). Example: calculate moles in 40.0 g Ca(OH)₂. Molar mass = 40.08 + 2×(16.00 + 1.008) = 40.08 + 34.016 = 74.10 g/mol. n = 40.0/74.10 = 0.540 mol. Going back to mass: 0.540 mol × 74.10 g/mol = 40.0 g ✓. Memorize: molar mass (g/mol) = numerically the same as the molecular weight (amu or Daltons).

Molecules = moles × 6.022 × 10²³. Moles = molecules / 6.022 × 10²³. Example: how many water molecules in 2.5 mol H₂O? Molecules = 2.5 × 6.022 × 10²³ = 1.506 × 10²⁴ molecules. How many moles is 1.00 × 10²¹ atoms of gold? n = 1.00 × 10²¹ / 6.022 × 10²³ = 1.66 × 10⁻³ mol = 1.66 mmol. Mass of gold = 1.66 × 10⁻³ × 196.97 = 0.327 g.

Balanced equations express molar ratios directly. Steps: (1) Write and balance the equation. (2) Convert given quantities to moles. (3) Use molar ratios from equation to find moles of desired substance. (4) Convert back to requested units. Example: 2H₂ + O₂ → 2H₂O. How much water from 10.0 g H₂? n(H₂) = 10.0/2.016 = 4.96 mol. From ratio H₂:H₂O = 2:2 = 1:1: n(H₂O) = 4.96 mol. Mass H₂O = 4.96 × 18.015 = 89.4 g. This molar approach works for all chemical calculations regardless of the scale of the reaction.